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Reaction force of an arched hinge structure, when a uniform distribution load is applied

작성자 Uploader : orion 작성일 Upload Date: 2019-11-13변경일 Update Date: 2020-01-06조회수 View : 375

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Find the reaction forces at points A and B when a uniform distribution load w (kN / m) is applied to the arched hinge structure as shown in the figure.

Assume that the vertical reactions at the hinges A and B are VA and VB and upward direction is positive (↑: +), and that the horizontal reactions are HA and HB and the right direction is positive (→: +). 		No Image

■ Data input : w (kN/m), L (m), H (m)



Since the sum of moments at the hinge A is zero,
∑MA = w*2L*L - VB*2L = 0

Then,



Sine the sum of vertical forces is zero,
VA = w*2L - VB

Then,



Since the sum of moments at the hinge C is zero, considering he left part,
∑MC = VA*L - w*L*L/2 - HA*H = 0

Then,


Since the sum of horizontal forces is zero and HA + HB = 0,
HB is obtained as follows.


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